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## G = C7⋊Dic12order 336 = 24·3·7

### The semidirect product of C7 and Dic12 acting via Dic12/Dic6=C2

Aliases: C213Q16, C28.8D6, C72Dic12, C42.12D4, C14.9D12, C12.25D14, Dic6.1D7, C84.18C22, Dic42.4C2, C7⋊C8.S3, C4.11(S3×D7), C31(C7⋊Q16), C6.4(C7⋊D4), C2.7(C7⋊D12), (C7×Dic6).1C2, (C3×C7⋊C8).1C2, SmallGroup(336,40)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C84 — C7⋊Dic12
 Chief series C1 — C7 — C21 — C42 — C84 — C3×C7⋊C8 — C7⋊Dic12
 Lower central C21 — C42 — C84 — C7⋊Dic12
 Upper central C1 — C2 — C4

Generators and relations for C7⋊Dic12
G = < a,b,c | a7=b24=1, c2=b12, bab-1=a-1, ac=ca, cbc-1=b-1 >

Smallest permutation representation of C7⋊Dic12
Regular action on 336 points
Generators in S336
(1 238 128 154 64 183 324)(2 325 184 65 155 129 239)(3 240 130 156 66 185 326)(4 327 186 67 157 131 217)(5 218 132 158 68 187 328)(6 329 188 69 159 133 219)(7 220 134 160 70 189 330)(8 331 190 71 161 135 221)(9 222 136 162 72 191 332)(10 333 192 49 163 137 223)(11 224 138 164 50 169 334)(12 335 170 51 165 139 225)(13 226 140 166 52 171 336)(14 313 172 53 167 141 227)(15 228 142 168 54 173 314)(16 315 174 55 145 143 229)(17 230 144 146 56 175 316)(18 317 176 57 147 121 231)(19 232 122 148 58 177 318)(20 319 178 59 149 123 233)(21 234 124 150 60 179 320)(22 321 180 61 151 125 235)(23 236 126 152 62 181 322)(24 323 182 63 153 127 237)(25 216 285 243 73 103 304)(26 305 104 74 244 286 193)(27 194 287 245 75 105 306)(28 307 106 76 246 288 195)(29 196 265 247 77 107 308)(30 309 108 78 248 266 197)(31 198 267 249 79 109 310)(32 311 110 80 250 268 199)(33 200 269 251 81 111 312)(34 289 112 82 252 270 201)(35 202 271 253 83 113 290)(36 291 114 84 254 272 203)(37 204 273 255 85 115 292)(38 293 116 86 256 274 205)(39 206 275 257 87 117 294)(40 295 118 88 258 276 207)(41 208 277 259 89 119 296)(42 297 120 90 260 278 209)(43 210 279 261 91 97 298)(44 299 98 92 262 280 211)(45 212 281 263 93 99 300)(46 301 100 94 264 282 213)(47 214 283 241 95 101 302)(48 303 102 96 242 284 215)
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24)(25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48)(49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72)(73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96)(97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120)(121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144)(145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168)(169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192)(193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216)(217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240)(241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264)(265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288)(289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312)(313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336)
(1 41 13 29)(2 40 14 28)(3 39 15 27)(4 38 16 26)(5 37 17 25)(6 36 18 48)(7 35 19 47)(8 34 20 46)(9 33 21 45)(10 32 22 44)(11 31 23 43)(12 30 24 42)(49 80 61 92)(50 79 62 91)(51 78 63 90)(52 77 64 89)(53 76 65 88)(54 75 66 87)(55 74 67 86)(56 73 68 85)(57 96 69 84)(58 95 70 83)(59 94 71 82)(60 93 72 81)(97 169 109 181)(98 192 110 180)(99 191 111 179)(100 190 112 178)(101 189 113 177)(102 188 114 176)(103 187 115 175)(104 186 116 174)(105 185 117 173)(106 184 118 172)(107 183 119 171)(108 182 120 170)(121 284 133 272)(122 283 134 271)(123 282 135 270)(124 281 136 269)(125 280 137 268)(126 279 138 267)(127 278 139 266)(128 277 140 265)(129 276 141 288)(130 275 142 287)(131 274 143 286)(132 273 144 285)(145 244 157 256)(146 243 158 255)(147 242 159 254)(148 241 160 253)(149 264 161 252)(150 263 162 251)(151 262 163 250)(152 261 164 249)(153 260 165 248)(154 259 166 247)(155 258 167 246)(156 257 168 245)(193 217 205 229)(194 240 206 228)(195 239 207 227)(196 238 208 226)(197 237 209 225)(198 236 210 224)(199 235 211 223)(200 234 212 222)(201 233 213 221)(202 232 214 220)(203 231 215 219)(204 230 216 218)(289 319 301 331)(290 318 302 330)(291 317 303 329)(292 316 304 328)(293 315 305 327)(294 314 306 326)(295 313 307 325)(296 336 308 324)(297 335 309 323)(298 334 310 322)(299 333 311 321)(300 332 312 320)

G:=sub<Sym(336)| (1,238,128,154,64,183,324)(2,325,184,65,155,129,239)(3,240,130,156,66,185,326)(4,327,186,67,157,131,217)(5,218,132,158,68,187,328)(6,329,188,69,159,133,219)(7,220,134,160,70,189,330)(8,331,190,71,161,135,221)(9,222,136,162,72,191,332)(10,333,192,49,163,137,223)(11,224,138,164,50,169,334)(12,335,170,51,165,139,225)(13,226,140,166,52,171,336)(14,313,172,53,167,141,227)(15,228,142,168,54,173,314)(16,315,174,55,145,143,229)(17,230,144,146,56,175,316)(18,317,176,57,147,121,231)(19,232,122,148,58,177,318)(20,319,178,59,149,123,233)(21,234,124,150,60,179,320)(22,321,180,61,151,125,235)(23,236,126,152,62,181,322)(24,323,182,63,153,127,237)(25,216,285,243,73,103,304)(26,305,104,74,244,286,193)(27,194,287,245,75,105,306)(28,307,106,76,246,288,195)(29,196,265,247,77,107,308)(30,309,108,78,248,266,197)(31,198,267,249,79,109,310)(32,311,110,80,250,268,199)(33,200,269,251,81,111,312)(34,289,112,82,252,270,201)(35,202,271,253,83,113,290)(36,291,114,84,254,272,203)(37,204,273,255,85,115,292)(38,293,116,86,256,274,205)(39,206,275,257,87,117,294)(40,295,118,88,258,276,207)(41,208,277,259,89,119,296)(42,297,120,90,260,278,209)(43,210,279,261,91,97,298)(44,299,98,92,262,280,211)(45,212,281,263,93,99,300)(46,301,100,94,264,282,213)(47,214,283,241,95,101,302)(48,303,102,96,242,284,215), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72)(73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96)(97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144)(145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192)(193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216)(217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240)(241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264)(265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288)(289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312)(313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336), (1,41,13,29)(2,40,14,28)(3,39,15,27)(4,38,16,26)(5,37,17,25)(6,36,18,48)(7,35,19,47)(8,34,20,46)(9,33,21,45)(10,32,22,44)(11,31,23,43)(12,30,24,42)(49,80,61,92)(50,79,62,91)(51,78,63,90)(52,77,64,89)(53,76,65,88)(54,75,66,87)(55,74,67,86)(56,73,68,85)(57,96,69,84)(58,95,70,83)(59,94,71,82)(60,93,72,81)(97,169,109,181)(98,192,110,180)(99,191,111,179)(100,190,112,178)(101,189,113,177)(102,188,114,176)(103,187,115,175)(104,186,116,174)(105,185,117,173)(106,184,118,172)(107,183,119,171)(108,182,120,170)(121,284,133,272)(122,283,134,271)(123,282,135,270)(124,281,136,269)(125,280,137,268)(126,279,138,267)(127,278,139,266)(128,277,140,265)(129,276,141,288)(130,275,142,287)(131,274,143,286)(132,273,144,285)(145,244,157,256)(146,243,158,255)(147,242,159,254)(148,241,160,253)(149,264,161,252)(150,263,162,251)(151,262,163,250)(152,261,164,249)(153,260,165,248)(154,259,166,247)(155,258,167,246)(156,257,168,245)(193,217,205,229)(194,240,206,228)(195,239,207,227)(196,238,208,226)(197,237,209,225)(198,236,210,224)(199,235,211,223)(200,234,212,222)(201,233,213,221)(202,232,214,220)(203,231,215,219)(204,230,216,218)(289,319,301,331)(290,318,302,330)(291,317,303,329)(292,316,304,328)(293,315,305,327)(294,314,306,326)(295,313,307,325)(296,336,308,324)(297,335,309,323)(298,334,310,322)(299,333,311,321)(300,332,312,320)>;

G:=Group( (1,238,128,154,64,183,324)(2,325,184,65,155,129,239)(3,240,130,156,66,185,326)(4,327,186,67,157,131,217)(5,218,132,158,68,187,328)(6,329,188,69,159,133,219)(7,220,134,160,70,189,330)(8,331,190,71,161,135,221)(9,222,136,162,72,191,332)(10,333,192,49,163,137,223)(11,224,138,164,50,169,334)(12,335,170,51,165,139,225)(13,226,140,166,52,171,336)(14,313,172,53,167,141,227)(15,228,142,168,54,173,314)(16,315,174,55,145,143,229)(17,230,144,146,56,175,316)(18,317,176,57,147,121,231)(19,232,122,148,58,177,318)(20,319,178,59,149,123,233)(21,234,124,150,60,179,320)(22,321,180,61,151,125,235)(23,236,126,152,62,181,322)(24,323,182,63,153,127,237)(25,216,285,243,73,103,304)(26,305,104,74,244,286,193)(27,194,287,245,75,105,306)(28,307,106,76,246,288,195)(29,196,265,247,77,107,308)(30,309,108,78,248,266,197)(31,198,267,249,79,109,310)(32,311,110,80,250,268,199)(33,200,269,251,81,111,312)(34,289,112,82,252,270,201)(35,202,271,253,83,113,290)(36,291,114,84,254,272,203)(37,204,273,255,85,115,292)(38,293,116,86,256,274,205)(39,206,275,257,87,117,294)(40,295,118,88,258,276,207)(41,208,277,259,89,119,296)(42,297,120,90,260,278,209)(43,210,279,261,91,97,298)(44,299,98,92,262,280,211)(45,212,281,263,93,99,300)(46,301,100,94,264,282,213)(47,214,283,241,95,101,302)(48,303,102,96,242,284,215), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72)(73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96)(97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144)(145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192)(193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216)(217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240)(241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264)(265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288)(289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312)(313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336), (1,41,13,29)(2,40,14,28)(3,39,15,27)(4,38,16,26)(5,37,17,25)(6,36,18,48)(7,35,19,47)(8,34,20,46)(9,33,21,45)(10,32,22,44)(11,31,23,43)(12,30,24,42)(49,80,61,92)(50,79,62,91)(51,78,63,90)(52,77,64,89)(53,76,65,88)(54,75,66,87)(55,74,67,86)(56,73,68,85)(57,96,69,84)(58,95,70,83)(59,94,71,82)(60,93,72,81)(97,169,109,181)(98,192,110,180)(99,191,111,179)(100,190,112,178)(101,189,113,177)(102,188,114,176)(103,187,115,175)(104,186,116,174)(105,185,117,173)(106,184,118,172)(107,183,119,171)(108,182,120,170)(121,284,133,272)(122,283,134,271)(123,282,135,270)(124,281,136,269)(125,280,137,268)(126,279,138,267)(127,278,139,266)(128,277,140,265)(129,276,141,288)(130,275,142,287)(131,274,143,286)(132,273,144,285)(145,244,157,256)(146,243,158,255)(147,242,159,254)(148,241,160,253)(149,264,161,252)(150,263,162,251)(151,262,163,250)(152,261,164,249)(153,260,165,248)(154,259,166,247)(155,258,167,246)(156,257,168,245)(193,217,205,229)(194,240,206,228)(195,239,207,227)(196,238,208,226)(197,237,209,225)(198,236,210,224)(199,235,211,223)(200,234,212,222)(201,233,213,221)(202,232,214,220)(203,231,215,219)(204,230,216,218)(289,319,301,331)(290,318,302,330)(291,317,303,329)(292,316,304,328)(293,315,305,327)(294,314,306,326)(295,313,307,325)(296,336,308,324)(297,335,309,323)(298,334,310,322)(299,333,311,321)(300,332,312,320) );

G=PermutationGroup([[(1,238,128,154,64,183,324),(2,325,184,65,155,129,239),(3,240,130,156,66,185,326),(4,327,186,67,157,131,217),(5,218,132,158,68,187,328),(6,329,188,69,159,133,219),(7,220,134,160,70,189,330),(8,331,190,71,161,135,221),(9,222,136,162,72,191,332),(10,333,192,49,163,137,223),(11,224,138,164,50,169,334),(12,335,170,51,165,139,225),(13,226,140,166,52,171,336),(14,313,172,53,167,141,227),(15,228,142,168,54,173,314),(16,315,174,55,145,143,229),(17,230,144,146,56,175,316),(18,317,176,57,147,121,231),(19,232,122,148,58,177,318),(20,319,178,59,149,123,233),(21,234,124,150,60,179,320),(22,321,180,61,151,125,235),(23,236,126,152,62,181,322),(24,323,182,63,153,127,237),(25,216,285,243,73,103,304),(26,305,104,74,244,286,193),(27,194,287,245,75,105,306),(28,307,106,76,246,288,195),(29,196,265,247,77,107,308),(30,309,108,78,248,266,197),(31,198,267,249,79,109,310),(32,311,110,80,250,268,199),(33,200,269,251,81,111,312),(34,289,112,82,252,270,201),(35,202,271,253,83,113,290),(36,291,114,84,254,272,203),(37,204,273,255,85,115,292),(38,293,116,86,256,274,205),(39,206,275,257,87,117,294),(40,295,118,88,258,276,207),(41,208,277,259,89,119,296),(42,297,120,90,260,278,209),(43,210,279,261,91,97,298),(44,299,98,92,262,280,211),(45,212,281,263,93,99,300),(46,301,100,94,264,282,213),(47,214,283,241,95,101,302),(48,303,102,96,242,284,215)], [(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24),(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48),(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72),(73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96),(97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120),(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144),(145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168),(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192),(193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216),(217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240),(241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264),(265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288),(289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312),(313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336)], [(1,41,13,29),(2,40,14,28),(3,39,15,27),(4,38,16,26),(5,37,17,25),(6,36,18,48),(7,35,19,47),(8,34,20,46),(9,33,21,45),(10,32,22,44),(11,31,23,43),(12,30,24,42),(49,80,61,92),(50,79,62,91),(51,78,63,90),(52,77,64,89),(53,76,65,88),(54,75,66,87),(55,74,67,86),(56,73,68,85),(57,96,69,84),(58,95,70,83),(59,94,71,82),(60,93,72,81),(97,169,109,181),(98,192,110,180),(99,191,111,179),(100,190,112,178),(101,189,113,177),(102,188,114,176),(103,187,115,175),(104,186,116,174),(105,185,117,173),(106,184,118,172),(107,183,119,171),(108,182,120,170),(121,284,133,272),(122,283,134,271),(123,282,135,270),(124,281,136,269),(125,280,137,268),(126,279,138,267),(127,278,139,266),(128,277,140,265),(129,276,141,288),(130,275,142,287),(131,274,143,286),(132,273,144,285),(145,244,157,256),(146,243,158,255),(147,242,159,254),(148,241,160,253),(149,264,161,252),(150,263,162,251),(151,262,163,250),(152,261,164,249),(153,260,165,248),(154,259,166,247),(155,258,167,246),(156,257,168,245),(193,217,205,229),(194,240,206,228),(195,239,207,227),(196,238,208,226),(197,237,209,225),(198,236,210,224),(199,235,211,223),(200,234,212,222),(201,233,213,221),(202,232,214,220),(203,231,215,219),(204,230,216,218),(289,319,301,331),(290,318,302,330),(291,317,303,329),(292,316,304,328),(293,315,305,327),(294,314,306,326),(295,313,307,325),(296,336,308,324),(297,335,309,323),(298,334,310,322),(299,333,311,321),(300,332,312,320)]])

42 conjugacy classes

 class 1 2 3 4A 4B 4C 6 7A 7B 7C 8A 8B 12A 12B 14A 14B 14C 21A 21B 21C 24A 24B 24C 24D 28A 28B 28C 28D ··· 28I 42A 42B 42C 84A ··· 84F order 1 2 3 4 4 4 6 7 7 7 8 8 12 12 14 14 14 21 21 21 24 24 24 24 28 28 28 28 ··· 28 42 42 42 84 ··· 84 size 1 1 2 2 12 84 2 2 2 2 14 14 2 2 2 2 2 4 4 4 14 14 14 14 4 4 4 12 ··· 12 4 4 4 4 ··· 4

42 irreducible representations

 dim 1 1 1 1 2 2 2 2 2 2 2 2 2 4 4 4 4 type + + + + + + + + - + + - + - + - image C1 C2 C2 C2 S3 D4 D6 D7 Q16 D12 D14 Dic12 C7⋊D4 S3×D7 C7⋊Q16 C7⋊D12 C7⋊Dic12 kernel C7⋊Dic12 C3×C7⋊C8 C7×Dic6 Dic42 C7⋊C8 C42 C28 Dic6 C21 C14 C12 C7 C6 C4 C3 C2 C1 # reps 1 1 1 1 1 1 1 3 2 2 3 4 6 3 3 3 6

Matrix representation of C7⋊Dic12 in GL6(𝔽337)

 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 336 303 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 0 1 0 0 0 0 336 336 0 0 0 0 0 0 308 249 0 0 0 0 224 29 0 0 0 0 0 0 0 319 0 0 0 0 206 311
,
 106 201 0 0 0 0 95 231 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 25 139 0 0 0 0 204 312

G:=sub<GL(6,GF(337))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,336,0,0,0,0,1,303,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,336,0,0,0,0,1,336,0,0,0,0,0,0,308,224,0,0,0,0,249,29,0,0,0,0,0,0,0,206,0,0,0,0,319,311],[106,95,0,0,0,0,201,231,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,25,204,0,0,0,0,139,312] >;

C7⋊Dic12 in GAP, Magma, Sage, TeX

C_7\rtimes {\rm Dic}_{12}
% in TeX

G:=Group("C7:Dic12");
// GroupNames label

G:=SmallGroup(336,40);
// by ID

G=gap.SmallGroup(336,40);
# by ID

G:=PCGroup([6,-2,-2,-2,-2,-3,-7,24,73,55,116,50,490,10373]);
// Polycyclic

G:=Group<a,b,c|a^7=b^24=1,c^2=b^12,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

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